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# The area of the trapezium is 1586 sq. m. The length of its parallel sides are 38 cm and 84 cm. Find the distance between them.

Last updated date: 14th Sep 2024
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Hint: Here, we will draw the diagram using the given information. We will substitute the given values in the formula of area of trapezium. Then we will simplify it to find the distance between the parallel sides by using the area of the trapezium formula. Area of the trapezium is defined as the region covered by the trapezium.

Formula Used:
We will use the formula Area of the Trapezium $= \dfrac{1}{2} \times \left( {a + b} \right) \times h$ , where $a$ and $b$ are the parallel sides and $h$ is the perpendicular distance between the parallel sides.

First we will draw the diagram of the trapezium based on the given information.

We will substitute the length of the parallel sides and in the formula for area of trapezium.
Substituting $a = 38$, $b = 84$ and $A = 1586$ in the formula Area of the Trapezium $= \dfrac{1}{2} \times \left( {a + b} \right) \times h$, we get
$\Rightarrow 1586 = \dfrac{1}{2} \times \left( {38 + 84} \right) \times h$
$\Rightarrow 1586 = \dfrac{1}{2} \times 122 \times h$
$\Rightarrow 1586 = 61 \times h$
$\Rightarrow h = \dfrac{{1586}}{{61}}$
$\Rightarrow h = 26{\rm{cm}}$